A former US official told the AP news agency that an American envoy sent to retrieve Mr Warmbier signed an agreement to pay the $2m on Mr Trump's instructions.

The president denied the claim, tweeting: "No money was paid to North Korea for Otto Warmbier, not two Million Dollars, not anything else."

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No money was paid to North Korea for Otto Warmbier, not two Million Dollars, not anything else. This is not the Obama Administration that paid 1.8 Billion Dollars for four hostages, or gave five terroist hostages plus, who soon went back to battle, for traitor Sgt. Bergdahl!

“President Donald J. Trump is the greatest hostage negotiator that I know of in the history of the United States. 20 hostages, many in impossible circumstances, have been released in last two years. No money was paid.” Cheif Hostage Negotiator, USA!

Mr Trump also boasted of being "the greatest hostage negotiator" in US history, quoting an unnamed chief hostage negotiator as saying so. (Social media users were quick to notice the misspelling of "chief" in Mr Trump's tweet, sending the word "cheif" trending on Twitter).

Mr Warmbier, a college student, was detained in a North Korean prison for 17 months after being convicted of trying to steal a propaganda poster while travelling as part of a tour group.

He was flown out of Pyongyang in a coma on 13 June 2017, but died six days later.

The medical bill imposed by North Korea went to the US Treasury in 2017 but remained unpaid throughout the year, according to The Washington Post.

Image:President Trump is believed to have signed off orders to pay medical costs

It is not clear whether the Trump administration's alleged payment was addressed during preparations for Mr Trump's two summits with North Korean leader Kim Jong Un.

US policy is to refuse to pay ransoms for the release of Americans detained abroad.

State department envoy Joseph Yun told CNN he was given orders to secure Mr Warmbier's release and believed the instructions came directly from Mr Trump.

"Yes, my orders were completely: do whatever you can to get Otto back," he said.

Speaking in March, the parents of the 22-year-old student said the North Korean regime was responsible for Mr Warmbier's death.

Fred and Cindy Warmbier said: "Kim and his evil regime are responsible for unimaginable cruelty and inhumanity. No excuses or lavish praise can change that."

Image:The 22-year-old student died in 2017 just six days after being returned to the US

A US coroner said the student died from a lack of oxygen and blood to the brain, disputing Pyongyang's claims he had contracted botulism and taken a sleeping pill.

North Korea also denied allegations by relatives that Mr Warmbier was tortured, saying he was provided "medical treatments and care with all sincerity".

Senator Rob Portman said the US does not owe North Korea anything.

He said: "Otto Warmbier was mistreated by North Korea in so many ways, including his wrongful conviction and harsh sentence, and the fact that for 16 months they refused to tell his family or our country about his dire condition they caused."